Running curve creation device, running curve creation method and running curve control program

ABSTRACT

A running curve creation device of an embodiment is a running curve creation device to create a running curve which can make a train having a prescribed vehicle characteristic run between a prescribed departure station and a prescribed arrival station in a prescribed running time with a smaller cumulative energy consumption. A shortest time running curve creation unit creates a shortest time running curve in which the train runs between the stations in a shortest time, based on predetermined vehicle information and ground information of the train, and an energy saving running curve creation unit selects from the shortest time running curve and a plurality of solution candidates corresponding to states of the train at each prescribed elapsed time since the train has departed from the departure station, a solution candidate having the relatively small cumulative energy consumption in the prescribed running time, and creates an energy saving running curve based on the selected solution candidate.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based upon and claims the benefit of priority fromthe prior Japanese Patent Application No. 2013-151104, filed on Jul. 19,2013; the entire contents of which are incorporated herein by reference.

This application is a continuation application of International PatentApplication No. PCT/JP2013/005289, filed on Sep. 6, 2013.

FIELD

The present embodiment relates to a running curve creation device, arunning curve creation method and a running curve control program.

BACKGROUND

Further energy saving (hereinafter, simply called energy saving) hasbeen demanded for a railway with excellent energy efficiency, due topower shortage in recent years. That is, the energy saving in a railwayis to change an auxiliary machine such as air-conditioning and lightingto an equipment with excellent energy efficiency, and to reduce energyat the time of running of a train, and so on. Particularly, the energysaving at the time of running of a train has been considered since longago, and it has variously been discussed in the reference documentslisted below.

Generally, the following three policies are taken in many cases, in theenergy saving relating to an operation of a train.

(1) To accelerate a train at a maximum acceleration at the time ofdeparting from a departure station.

(2) To preferably increase coasting (inertia running) within a speedlimitation.

(3) To decelerate a train at a maximum deceleration at the time ofreaching a station.

Regarding these fundamental policies, various energy saving runningcurve creation methods have been proposed so far. In order to create arunning curve based on these fundamental policies, many methods tocreate a running curve by a heuristic have been proposed. However, in acase that a speed limitation is simple such as one maximum speed existsbetween stations, and in a case that a running time is larger comparedwith a shortest time, a running curve close to an optimum running curvecan be obtained even by a heuristic. However, in a case that the speedlimitation between stations is complicated, when a running curve iscreated by a heuristic, there is a case that a solution cannot beobtained, or only a solution may be obtained in which the energyconsumption is considerably larger than an optimum solution. For thereason, a method which can obtain a solution close to an optimumsolution has been desired, even if a given speed limitation and gradientare complicated.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic configuration diagram of a running curve creationdevice.

FIG. 2 is a schematic configuration diagram of the running curvecreation device when it is configured by a personal computer.

FIG. 3 is an explanation diagram of a format and a data example of theground information data.

FIG. 4 is an explanation diagram of a format and a data example of thevehicle information data.

FIG. 5 is a diagram showing a creation operation and a pruning operationin a combinational optimization problem.

FIG. 6 is a processing flow chart of an embodiment.

FIG. 7 is a creation processing flow chart of a shortest time runningcurve.

FIG. 8 is an explanation diagram of a usable condition of a maximumacceleration and a maximum deceleration.

FIG. 9 is a processing flow chart of a creation processing of anacceleration limit curve.

FIG. 10 is a processing flow chart of a creation processing of adeceleration limit curve.

FIG. 11 is a processing flow chart of a creation processing of ashortest time running curve.

FIG. 12 is a processing flow chart of a creation processing of an energysaving running curve.

FIG. 13 is an (x−t) graph wherein a time is taken on a horizontal axisand a position of a train is taken on a vertical axis.

FIG. 14 is an explanation diagram of a velocity condition.

FIG. 15 is an explanation diagram of a quantization processing.

FIG. 16 is an explanation diagram of a format and a data example of thestorage data of the running curve creation result storage unit.

FIG. 17 is a diagram of a running curve which has been visualized, basedon the storage data of the running curve creation result storage unit.

FIG. 18 is a diagram showing an example of the running curve to bedisplayed on a display.

DETAILED DESCRIPTION

A running curve creation device of an embodiment creates a running curvewhich can make a train having a prescribed vehicle characteristic runbetween a prescribed departure station and a prescribed arrival stationin a prescribed running time with a smaller cumulative energyconsumption.

And, a shortest time running curve creation unit creates a shortest timerunning curve in which the train runs between the stations in a shortesttime (shortest running time), based on predetermined vehicle informationand ground information of the train.

By this means, an energy saving running curve creation unit selects,from the shortest time running curve and a plurality of solutioncandidates corresponding to states of the train at each prescribedelapsed time since the train has departed from the departure station asolution candidate having the relatively small cumulative energyconsumption in the prescribed running time, and creates an energy savingrunning curve based on the selected solution candidate.

A running curve creation device of an embodiment can provide a runningcurve creation device capable of creating a running curve closer to anoptimum solution at high speed.

Next, further detailed embodiments will be described in detail withreference to the drawings.

FIG. 1 is a schematic configuration block diagram of a running curvecreation device.

A running curve creation device 10 is provided with a ground informationstorage unit 11 which previously stores ground information datadescribed later to become necessary for creating a running curve, avehicle information storage unit 12 which previously stores vehicleinformation data described later to become necessary for creating therunning curve, a running curve input processing unit 13 which inputsvarious data such as vehicle information, between-station information,running time information, acquires the ground information data to becomenecessary for creating the running curve based on the inputted data fromthe ground information storage unit 11, and acquires the vehicleinformation data from the vehicle information storage unit 12, ashortest time running curve creation unit 14 which creates a shortesttime running curve for running a train between designated stations in ashortest time, by a vehicle condition designated based on the variousdata inputted from the running curve input processing unit 13, an energysaving running curve creation unit 15 to create an energy saving runningcurve which makes a train run between the designated stations in thedesignated running time based on the shortest time running curve, andcan achieve energy saving, a running curve creation result storage unit16 which stores the shortest time running curve which the shortest timerunning curve creation unit 14 has created, and the running curve whichthe energy saving running curve creation unit 15 has created, and arunning curve creation result display unit 17 to display the runningcurve creation result which the energy saving running curve creationunit 15 has created.

In the present embodiment, it is supposed that the running curve iscreated by a general-purpose personal computer or the like.

FIG. 2 is a schematic configuration block diagram of the running curvecreation device when it is configured by a personal computer.

As shown in FIG. 2, the running curve creation device 10 is providedwith an MPU 21 which is configured as a microcomputer to control thewhole running curve creation device, and functions as the running curveinput processing unit 13, the shortest time running curve creation unit14 and the energy saving running curve creation unit 15, a ROM 22 whichstores various data including a control program in a non-volatilemanner, a RAM 23 which is used as a working area of the MPU 21, andtemporarily stores various data, an external storage device 24 which isconfigured as a hard disk drive device (HDD) or the like, and functionsas the ground information storage unit 11, the vehicle informationstorage unit 12 and the running curve creation result storage unit 16,an IC card reader/writer (R/W) 26 which is readable and writable variousdata to an IC memory that is a semiconductor storage device, and canfunction as the running curve input processing unit 13, a keyboard 27from which an operator can input various information, and which canfunction as the running curve input processing unit 13, a display 28which is configured as a liquid crystal display, an organic EL displayor the like, and can function as the running curve creation resultdisplay unit 17, and a communication interface (I/F) 29 which performsan interface operation of communication via a communication network suchas Internet, a LAN not shown, and can function as the running curveinput processing unit 13.

Here, a format and a data example of the storage data in each of theground information storage unit 11 and the vehicle information storageunit 12 will be described.

To begin with, a format and a data example of the ground informationdata stored in the ground information storage unit 11 will be described.

FIG. 3 is an explanation diagram of a format and a data example of theground information data.

When broadly divided, ground information data 30 which is stored in theground information storage unit 11 includes ground ID data 31 forspecifying the ground information data, station related data 32including station related information corresponding to the relevantground information data 30, speed limitation data 33 as informationrelating to speed limitation between the stations corresponding to thestation related data 32, and gradient data 34 as information relating toa gradient between the stations corresponding to the station relateddata.

The station related data 32 includes between-station information data 35corresponding to the ground ID data 31, and between-station distancedata 36 corresponding to the ground ID data 31.

More specifically, the between-station information data 35 indicates togo from A station toward B station, and the between-station distancedata 36 indicates that a between-station distance in the case of goingfrom A station toward B station is 1500 m.

With respect to a limitation of a speed between the stations specifiedby the station related data 32, the speed limitation data 33 includesstarting point data 37 indicating a starting point of a speed limitationsection where a speed limitation is imposed, end point data 38indicating an end point of the speed limitation section, and speed data39 indicating an upper limit speed in the relevant speed limitationsection.

The starting point data 37 indicates a distance from a departure stationto a starting point position of the speed limitation section, when thedeparture station (in the above-described case, A station) is set to 0m.

In addition, the end point data 38 indicates a distance from thedeparture station to an end point position of the speed limitationsection, when the departure station is set to 0 m.

In addition, an upper limit speed value in the corresponding speedlimitation section is stored in the speed data 39.

Specifically, in the case of the example of FIG. 3, regarding the speedlimitation section, there are four sections between A station that isthe departure station and B station that is the arrival station, and afirst section is a section from a position (distance 0 m) of A stationthat is the departure station to a position of 500 m therefrom, and theupper limit speed value is 25 m/sec.

Similarly, a second section is a section from a position of 500 m fromthe departure station to a position of 750 m therefrom, and the upperlimit speed value is 23 m/sec. A third section is a section from aposition of 1000 m from the departure station to a position of 1300 mtherefrom, and the upper limit speed value is 20 m/sec. A fourth sectionis a section from a position of 1300 m from the departure station to aposition of 1500 m (the position of B station that is the end pointstation) therefrom, and the upper limit speed value is 20 m/sec.

The gradient data 34 includes all gradient information from thedeparture station to the arrival station, and is provided with startingpoint data 40 indicating a starting point of a section where a gradientis continuously constant, end point data 41 indicating an end point ofthe section where the relevant gradient is continuously constant, andgradient value data 42 indicating a gradient value in the relevantgradient constant section.

Specifically, in the case of an example of FIG. 3, regarding thegradient constant section, there are three sections between A stationand B station, and a first section is a section from a position(distance 0 m) of A station that is the departure station to a positionof 1000 m therefrom, and the gradient value is 0%.

Similarly, a second section is a section from a position of 1000 m fromthe departure station to a position of 1300 in therefrom, and thegradient value is 2. A third section is a section from a position of1300 in from the departure station to a position (the position of Bstation that is the arrival station) of 1500 m therefrom, and thegradient value is 0%.

Next, a format and a data example of the vehicle information data storedin the vehicle information storage unit 12 will be described.

FIG. 4 is an explanation diagram of a format and a data example of thevehicle information data.

Vehicle information data 50 stored in the vehicle information storageunit 12 includes vehicle ID data 51 for specifying a railway vehicle,type data 52 indicating a driving type of the railway vehicle, vehiclebody weight data 53 indicating a weight of a vehicle body, riding ratedata 54 indicating a riding rate which is supposed at the time ofcreating a running curve, formation vehicle number data 55 indicatingthe number of the railway vehicles in a formation, train length data 56indicating a train length, and notch characteristic ID data 57 forspecifying notch characteristic of a master controller mounted on therelevant railway vehicle.

Specifically, in the case of the example of FIG. 4, the vehicle ID data51=5, the type data 52 indicates that a driving type of the railwayvehicle is a VVVF system, the vehicle body weight data 53 indicates thatthe vehicle body weight is 10 t, the riding rate data 54 indicates thata riding rate which is supposed at the time of creating a running curveis 50%, the formation vehicle number data 55 indicates that the numberof the vehicles in a formation is 10, the train length data 56 indicatesthat a train length is 200 m, and the notch characteristic ID data 57indicates that the notch characteristic ID of the master controllermounted on the relevant railway vehicle=5.

Next, prior to explaining an operation of the embodiment, a principledthinking of the embodiment will be described.

An energy saving running curve of a train has an equation of motionincluding a running resistance and a gradient resistance, and so on asconstraints, and two-point boundary values wherein a state (initialstate) at a departure station (t, v, x)=(0, 0, 0), and a state (terminalstate) at an arrival station (t, v, x)=(T, 0, X), which are expressed byan elapsed time t after departure, a velocity v and a distance x fromthe departure station.

Here, T is an elapsed time required for a train to run from thedeparture station to the arrival station, and X is a distance betweenthe departure station and the arrival station.

On the other hand, an evaluation function can be obtained by solving anoptimum control problem for a total sum E (cumulative energyconsumption) of energy which is consumed between a departure station andan arrival station. At this time, a control variable to designate amotion of a train becomes a notch to designate acceleration,deceleration. A train which is spreading widely at present realizesacceleration and deceleration of the train by a plurality of notches,and a running curve can be regarded as a multistage decision-makingproblem as to which notch is to be selected for operation at each time.

By the way, a matter which generally becomes a problem at the time ofsolving a multistage decision-making problem is a combinationalexplosion of solution candidates.

Hereinafter, the combinational explosion will be described briefly.

For example, there are ten choices of a notch, and when a running curvein a running time 100 seconds is created while a minimum control timeunit is set to 1 second, a solution to satisfy the constraint has to befound from solution candidates of 10¹⁰⁰. It is impossible to find asolution to satisfy the constraint one by one from these within arealistic time range.

Accordingly, as a method to solve a problem of this combinationalexplosion, a searching method of an optimum solution using dynamicprogramming has been proposed.

Creation of a running curve using dynamic programming is a method inwhich a state of (time, velocity, position) of a train is defined on alattice point, and which searches a route of the lattice points in whichthe cumulative energy consumption becomes the smallest. At this time,when a plurality of routes to reach a certain state (t, v, x) exist,only a route in which the cumulative energy consumption is the smallestis stored, and the search is continued. When dynamic programming isused, a state space is previously divided in a lattice manner, butgenerally, it rarely occurs to move from a lattice point to anotherlattice point. For the reason, when it is not on a lattice point, anycorrection is made, and thereby it is assumed to have moved to a latticepoint. In this method, when corrections to a lattice point increase,there is a problem that an error increases compared with an optimumsolution.

Accordingly, in the present embodiment, a method is proposed which doesnot list up the whole of solution candidates of a multistagedecision-making problem, but while checking (pruning) whether to becable of becoming a candidate for a feasible solution at each stage(time), generates a solution candidate each time the stage is advanced.

Here, pruning is a general-purpose method for solving a combinationaloptimization problem which is known in the field of operations research.That is a method which generates a solution candidate in a generationoperation, prunes a solution candidate incapable of becoming an optimumsolution, and deletes such a solution candidate from a list of solutioncandidates. An optimum solution is searched, while repeating thegeneration operation and the pruning operation. This method is thinkingsimilar to total enumeration, but it is more effective than the totalenumeration method in that searching is not performed for one incapableof becoming a solution candidate.

FIG. 5 is a diagram showing a generation operation and a pruningoperation in the combinational optimization problem.

Specifically, when a state is a velocity V0, a position X0, at anelapsed time t=0, regarding the conceivable state, at an elapsed timet=1 after a minimum control time unit has elapsed, a first state is avelocity V1, a position X1, a second state is a velocity V2, a positionX2, a third state is a velocity V3, a position X3, but when evaluationof the relevant third state or three states (velocity V10, positionX10), (velocity V11, position X11), (velocity V12, position X12) at anelapsed time t=2 which have transited from the relevant third state isperformed, when an evaluation value required for making transitioncannot be obtained (when improbable as a solution candidate), pruning isperformed and the following search is not performed. However, since apruning operation changes depending on a problem to be solved, it has tobe properly set according to the problem.

Hereinafter, a specific operation including a generation operation and apruning operation will be described.

FIG. 6 is a processing flow chart of the embodiment.

To begin with, the ground information, the vehicle information and arunning time T are acquired from the running curve input processing unit13 (step S101).

That is, when creating a running curve, it is necessary to input whatbetween-station of a route (it is necessary to discriminate a case toadvance from A station to B station, and a case to advance from Bstation to A station), by what vehicle, and in what running time T, atrain is made to run.

Here, regarding inputting of various data such as the vehicleinformation, the between-station information, the running time, it isthought that a setting file stored in an IC card 25 is read by the ICcard R/W 26, or the data is inputted from a setting file received viathe communication I/F 29, or the data is directly inputted via akeyboard 27 or the like.

When the various data such as the vehicle information, thebetween-station information, the running time information is inputted tothe running curve input processing unit 13, the running curve inputprocessing unit 13 acquires data necessary for creating a running curve,with reference to the ground information storage unit 11 and the vehicleinformation storage unit 12, and based on the inputted vehicleinformation and between-station information.

Subsequently, the MPU 21 functioning as the shortest time running curvecreation unit 14 receives data necessary for creating a running curvefrom the running curve input processing unit 13, and creates a runningcurve of a shortest time between the inputted stations (step S102).

FIG. 7 is a creation processing flow chart of a shortest time runningcurve.

When roughly classified, the creation processing of a shortest timerunning curve is configured to be provided with a creation processing ofan acceleration limit curve (step S201), a creation processing of adeceleration limit curve (step S202) and a creation processing of ashortest time running curve by a pruning algorithm (step S203).

Hereinafter, this will be specifically described.

In order to create a shortest time running curve, it is necessary toobtain a solution of a shortest time control having an initial conditionand a terminal condition. Generally, the shortest time control iscontrolled by a maximum acceleration or a maximum deceleration, that iscalled bang-bang control. However, since a speed limitation mainly by aposition is applied at the time of operating a train, a train is notnecessarily be controlled by only a maximum acceleration and a maximumdeceleration. Accordingly, a range in which a train can be moved by amaximum acceleration or a maximum deceleration is obtained.

FIG. 8 is an explanation diagram of a usable condition of a maximumacceleration and a maximum deceleration.

Cases in which a maximum acceleration and a maximum deceleration can beused at the time of operating a train are four cases of case 1-case 4,as shown in FIG. 8.

Case 1: to use a maximum acceleration when departing from a departurestation

Case 2: to use a maximum deceleration when arriving at an arrivalstation

Case 3: to use a maximum acceleration when a speed increases in thetraveling direction

Case 4: to use a maximum deceleration when a speed limit decreases inthe traveling direction

In FIG. 8, a right upward line shows a case in which a train is moved ata maximum acceleration, and a right downward line shows a case in whicha train is moved at a maximum deceleration.

Only one state of Case 1 and only one state of Case 2 inevitably existin one between-station.

In contrast, since there is a possibility that a plurality of states ofCase 3 and a plurality of states of Case 4 exist in one between-station,it is necessary to calculate an acceleration limit curve and adeceleration limit curve for the whole of them.

Firstly, a variable ST shown in FIG. 9 and FIG. 10 will be describedusing FIG. 8.

To begin with, it is assumed that a velocity limitation is given by afollowing struct array.

struct velocity_limitation { double position; // starting position ofvelocity limitation double velocity; // velocity limit after the above-described starting positon }; In Fig. 8, struct velocity_limitationST[3] = {{0, vmax}, {x1, v2}, {x2, vmax}};

Here, it is assumed that the smaller an index of the struct is, thesmaller the starting position becomes, such asST[0].position<ST[1].position<ST[2].position<ST[3].position.

Next, positions to become targets of an acceleration limit curve and adeceleration limit curve are detected.

The followings are set by default.

a target position of the acceleration limit curve=0; // Case 1

a target velocity of the acceleration limit curve=0; // Case 1

a target position of the deceleration limit curve=x; // Case 2 (adistance from the departure station to the arrival station)

a target velocity of the deceleration limit curve=0; // Case: 2

Regarding others, positions which coincide with the following conditionsare set as target positions of the acceleration limit curve and thedeceleration limit curve.

for (int i = 1; i < sizeof(ST)/sizeof(ST[0]); i++) { if(ST[i−1].velocity < ST[i].velocity) { a target position of theacceleration limit curve = ST[i].position; // Case3 a target velocity ofthe acceleration limit curve = ST[i− 1].velocity; // Case3 } else { atarget position of the deceleration limit curve = ST[i].position; //Case4 a target velocity of the deceleration limit curve =ST[i].velocity; // Case3 } }

In FIG. 9, regarding the target positions and the target velocitiesnecessary for creating an acceleration limit curve, all target positionsand target velocities which satisfy the above-described conditions inCase 1 at the time point of departing from a station of default, and incases in which a plurality of velocity limitations exist, are set in thearray ST.

Similarly, in FIG. 10, regarding the target positions and the targetvelocities necessary for creating a deceleration limit curve, all targetpositions and target velocities which satisfy the above-describedconditions in Case: 2 at the time point of arriving at a station ofdefault, and in cases in which a plurality of velocity limitationsexist, are set in the array ST.

Specifically, FIG. 8 is taken as an example,

in the case of the acceleration limit curve,

struct velocity_limitation ST[2]={{0, 0}, {x2, v2}};

and in the case of the deceleration limit curve,

struct velocity_limitation ST[2]={{x1, v2}, {X, 0}};

In the acceleration limit curve creation processing (step S201), tobegin with, (velocity, position) is calculated when the maximumacceleration and the maximum deceleration are used.

Each curve in the case 1-the case 4 shown in FIG. 8 shall be called anacceleration limit curve or a deceleration limit curve.

By the way, the acceleration limit curve can easily be obtained bygiving an initial condition of a velocity and a position of a case touse a maximum acceleration.

FIG. 9 is a processing flow chart of a creation processing of anacceleration limit curve.

To begin with, a variable s is initialized, and is set to 0 of aninitial value (step S401).

Next, a target position of the acceleration limit curve, that is, anacceleration elapsed time i=0, an initial velocity in the accelerationlimit curve v(0) ST[s].velocity and an initial positionx(0)=ST[s].position are set (step S402).

Next, 1 is added to the time i (step S403).

Subsequently, a state (v(i), x(i)) at the time i is calculated bysolving the equation of motion by a maximum acceleration notch(corresponding to a notch position capable of obtaining a maximumacceleration) (step S404).

Next, whether the velocity v(i) at the time i has exceeded a velocitylimit vmax, that is v(i)>vmax, or whether or not the position x(i) atthe time i has exceeded the target position ST[s].position isdiscriminated (step S405).

In the discrimination of the step S405, when the velocity v(i) at thetime i does not exceed the velocity limit vmax, and the position x(i) atthe time i does not exceed the target position ST[s].position (stepS405; No), the processing is transferred to the step S403 again, andthen the similar processing is repeated.

In the discrimination of the step S405, when the velocity v(i) at thetime i exceeds the velocity limit vmax, or the position x(i) at the timei exceeds the target position ST[s].position (step S405; Yes),

whether or not the target position of the acceleration limit curve isreached is discriminated, that is, whether or not

s=sizeof(ST[s])/sizeof(ST[0])

is discriminated (step S406).

In the discrimination of the step S406, when the target position of theacceleration limit curve is not reached (step S406; No), 1 is added tothe variable s (step S407), and the processing is transferred to thestep S402 again, and then the similar processing is repeated.

In the discrimination of the step S406, when the target position of theacceleration limit curve is reached (step S406; Yes), the creationprocessing of the acceleration limit curve is finished.

Next, the deceleration limit curve is calculated in the same manner asthe calculation of the acceleration limit curve (step S202).

In the present embodiment, in the case of the deceleration limit curve,an initial condition which satisfies a terminal condition is searchedwith an iteration method. Generally, since it is almost impossible toaccurately coincide with a terminal condition, allowable ranges (ε andδ) are given to a terminal condition, and an initial condition tosatisfy the range is obtained.

FIG. 10 is a processing flow chart of a creation processing of adeceleration limit curve.

To begin with, the variable s is initialized and is set to 0 of aninitial value, a variable a is initialized and is set to 0 of an initialvalue, and a variable b=ST[s].position, a variableDistance=ST[s].position (step S501).

Next, a target position of the deceleration limit curve, that is, adeceleration elapsed time i=0, an initial velocity in the decelerationlimit curve v(0)=vmax and an initial position x(0)=(a+b)/2.0 are set(step S502).

Next, 1 is added to the time i (step S503).

And, a state of the train at the time i is calculated by solving theequation of motion by a maximum deceleration notch (step S504).

Subsequently, whether or not the velocity v(i) at the time i satisfiesthe following equation corresponding to the allowable value ε (stepS505).

0≦v(i)<ε

In the discrimination of the step S505, when e≦v(i) (step S505; No), theprocessing is transferred to the step S503 again, and then, the similarprocessing is performed.

In the discrimination of the step S505, when 0≦v(i)<ε (step S505; Yes),whether or not the position x(i) at the time i satisfies the followingequation corresponding to the allowable value δ (step S506).

|x(i)−Distance|<δ.

In the discrimination of the step S506, when |x(i)−Distance|δ (stepS506; No), whether or not x(i)<Distance is discriminated (step S507).

In the discrimination of the step S507, when x(i)<Distance (step S507;Yes), a=(a+b)/2.0, and the processing is transferred to the step S502again, and then, the similar processing is performed (step S508).

In the discrimination of the step S507, when x(i) Distance (step S507;No), b=(a b)/2.0, and the processing is transferred to the step S502again, and then, the similar processing is performed (step S509).

On the other hand, in the discrimination of the step S506, when|x(i)−Distance|<δ (step S506; Yes), whether or not the target positionof the deceleration limit curve has been reached is discriminated, thatis, whether or not s=sizeof(ST[s])/sizeof(ST[0]) is discriminated (stepS510).

In the discrimination of the step S510, when the target position of thedeceleration limit curve has not been reached (step S510; No), 1 isadded to the variable s (step S511), and the processing is transferredto the step S502 again, and then, the similar processing is repeated.

In the discrimination of the step S510, when the target position of thedeceleration limit curve has been reached (step S510; Yes), the creationprocessing of the deceleration limit curve is finished.

By the way, in order to calculate a deceleration limit curve, a reversemethod in which an equation of motion is solved while advancing a timebackward is used sometimes, but when a gradient exists, a solution bythe reverse method sometimes deviates from a solution by a generalnumerical solution method of a differential equation in which theequation is solved while advancing a time forward.

In contrast, according to the method of the present embodiment, a methodfor solving a differential equation more accurately is used, andthereby, compared with a reverse method, a deceleration limit curve withmore accuracy can be obtained.

Next, a shortest time running curve is created based on a pruningalgorithm (step S203).

FIG. 11 is a processing flow chart of a creation processing of ashortest time running curve.

Here, a variable previous_state, a variable current_state and a variablemiddle_state which are shown in FIG. 11 will be described.

In the present embodiment, a control program which has been developedwith a high-level language such as C++ and JAVA (registered trademark)is supposed, as a control program to realize a running curve creationprocessing.

Particularly, in C++ and JAVA, it is possible to use a variable lengtharray in which a size of an array can be varied depending on the numberof elements. For this reason, in the present embodiment, a solutioncandidate at each time shall be expressed using a variable length array.

Specifically, a solution candidate is expressed in C++ or the like by astruct such as

struct phase { double position; // position double velocity; // velocitydouble energy; // instantaneous energy consumption double total_energy;// cumulative energy consumption int notch[500]; // a notch number ateach time int change_count; // the number of times of notch changeoverint notch_continuous_time; // a continuous time of the present notch};.

And, by making

vector<struct phase>previous_state;

vector<struct phase>current_state;

vector<struct phase>middle_state;

a solution candidate should be expressed.

To begin with, the elapsed time t=0, the velocity v=0, the position x=0are set to the variable previous_state, as an initial condition of thedeparture station, (step S601).

Next, the equations of motion (differential equation) in the wholenotches are solved, for each of the solution candidates at the elapsedtime t+1, and thereby solution candidates at the elapsed time t arecreated by the number of (the number of solution candidates at theelapsed time t) X (notch selection number), and the solution candidatesare stored as the variable current_state, and the variableprevious_state is released (cleared) from the memory (step S602).

Here, a method of creating a solution candidate at the elapsed time t+1will be specifically described.

To begin with, it is assumed that N solution candidates exist at theelapsed time t.

When a state of an n-th solution candidate in N solution candidates isdescribed as (t, v_(n)(t), x_(n)(t)), a state at the elapsed time t+1 iscalculated by numerical calculation such as a quartic Runge-Kuttamethod, using an acceleration or a deceleration given by a k-th notchNOTCH(k), by setting the n-th state (t, v_(n)(t), x_(n)(t)) as aninitial value on numerical calculation. Here, a quartic Runge-Kuttamethod has been listed as the numerical calculation example, but anumerical solution method of an equation of motion is not limited tothis.

By this means, solution candidates at the elapsed time t+1 are generatedby NK pieces.

Subsequently, regarding a velocity of each of the solution candidates ofthe variable current_state, whether the velocity is a value smaller thanthe acceleration limit curve, the deceleration limit curve and avelocity limitation by the position is checked, and only those having asmaller velocity are stored in the variable middle_state, and thevariable current-state is released (cleared) from the memory (stepS603).

The variable middle_state is sorted in descending order (in order from alarger one) of the position, and the high order K pieces thereof arestored in the variable previou_state, and the variable middle_state isreleased from the memory (step S604).

Here, the higher order K pieces are left, because of preventing thesolution candidates from becoming nonexistent. The larger the value of Kis, the lower the possibility that the solution candidate becomesnonexistent is. However, if the value of K becomes too large, since thecalculation time becomes larger, and thereby it is thought thatpractically K=about 20 is proper.

Accordingly, in the following description, consideration will be madeassuming that K=20.

Further, the processing is repeated until the condition in which theterminal condition has an allowable width is satisfied (step S605; Yes),in the same manner as the deceleration limit curve, and t+1 is set to ashortest running time, for the elapsed time t when a solution candidateto satisfy the condition is found (step S607).

In the discrimination of the step S605, when the condition is notsatisfied (step S605; No), 1 is added to the elapsed time t(incremented) (step S606), and the processing is transferred to the stepS602 again, and then the similar processing is repeated.

Next, a creation processing of an energy saving running curve will bedescribed.

FIG. 12 is a processing flow chart of a creation processing of an energysaving running curve.

To begin with, in order to create an energy saving running curve in therunning time T which is inputted by the running curve input processingunit 13, the result of the shortest time running curve creation unit 14is acquired, and the result of the shortest time running curve is set asan upper limit value, and one which is obtained by moving the result ofthe shortest time running curve in the time direction by the runningtime T is set as a lower limit value (step S700).

To begin with, as an initial condition of a departure station, theelapsed time t=0, the velocity v=0, the position x=0 are set to thevariable previous_state (step S701).

Next, the equations of motion (differential equation) in the wholenotches are solved, for each of the solution candidates at the elapsedtime t+1, and thereby solution candidates at the elapsed time t arecreated by the number of (the number of solution candidates at theelapsed time t) X (notch selection number), and the solution candidatesare stored as the variable current_state, and the variableprevious_state is released (cleared) from the memory (step S702).

Subsequently, those satisfying a condition of a solution (position,velocity, number of times of notch changeover, notch continuous time),in the variable current_state are stored in the variable middle_state,and the variable current_state is released (cleared) from the memory(step S703).

The variable middle_state at the elapsed time t+1 is sorted by a state(quantized position, quantized velocity, number of times of notchchangeover). And one with the smallest cumulative energy consumptionamount among the states which are assumed to be the same state isselected as one of solution candidates, and is stored in the variableprevious_state, and then the variable middle_state is released from thememory (step S704).

Next, whether or not the elapsed time t=the running time T isdiscriminated (step S705).

In the discrimination of the step S705, when the elapsed time t<therunning time T yet (step S705; No), 1 is added to the elapsed time t (isincremented), and the processing is transferred to the step S702 again,and then the similar processing is repeated.

In the discrimination of the step S705, when the elapsed time t=therunning time T (step S705; Yes), one with the smallest cumulative energyconsumption amount out of the solution candidates stored in the variableprevious_state is selected as an optimum solution (step S707).

Next, a condition for checking a solution candidate will be described indetail.

For simplification, here it will be described to calculate a runningcurve in the case that a train has run between certain stations in arunning time T_(min)+10, as an example. Here, the shortest running timeT_(min) is a running time (shortest running time) when a train has runbetween the stations in a shortest time.

It is assumed that a train runs between the stations in a running timeT_(min)+10 which is 10 seconds longer than the shortest running timeT_(min).

FIG. 13 is an (x−t) graph wherein a time is taken on a horizontal axisand a position of a train is taken on a vertical axis.

An upper graph indicates the relation of the position x and the elapsedtime t in the case of running in the shortest running time T_(min), anda lower graph indicates the relation of the position x and the elapsedtime t in the case of running in the shortest running time T_(min),after waiting 10 seconds at a departure station.

Here, the shortest running time T_(min) is a time in the case that atrain is made to run by making the most of the performance of a vehicle,and if the performances of vehicles are the same, it indicates that atrain cannot run faster than that time.

That is, when the performance of a vehicle is determined, the shortestrunning time T_(min) can be obtained uniquely.

Accordingly, when the position x is closer to the departure station thanthe lower graph, it is indicated that a train cannot arrive at thearrival station (next station) in the running time T_(min)+10.

Accordingly, the following can be said.

When a train runs between certain stations in the running timeT_(min)+10, a position at the elapsed time t in the case that the trainruns in the shortest running time T_(min) between the stations is madeUpper[t], and a graph which is obtained by moving a graph (t, Upper[t])in the shortest running time T_(min) in parallel in the time axisdirection by 10 seconds is made (t, Lower[t]). In this regard, it isassumed that when t<10, Lower[t]=0.

When an orbit of a solution in which the energy consumption amount inthe running time T_(min)+10 becomes minimum is made (t, v(t), x(t)),

Lower[t]≦x(t)≦Upper[t]

is established.

Here, t is 0, 1, 2, . . . , T_(min)+10.

FIG. 14 is an explanation diagram of a velocity condition.

Generally, in the railway business world, this graph is called a runningcurve. Here, in the (v−x) graph, a velocity V at the position xcorresponding to the running time T is written as V_(T)[x]. Then, it isknown that the following characteristic exists, from the result of priorresearch.

0≦V _(T) [x]≦V _(Tmin) [x]

Here, 0≦x≦X

That is, when seen in the graph (v−x), the running curve of the runningtime T exists inside the shortest time running curve.

However, regarding a result of the shortest time running curve, only avelocity and a position of the train at a discrete elapsed time t areknown, and it is difficult to calculate such result in the same manneras V[x].

Accordingly, the following equation will be used, in place of theabove-described relational expression between V_(T)[x] and V_(Tmin)[x].To begin with, a velocity and a position at the elapsed time t for anoptimum running curve of the running time T_(min), are respectively madeV_(Tmin)(t), X_(Tmin)(t). α (natural number) which satisfiesX_(Tmin)(α−1)≦x(t)<X_(Tmin)(α) is to be found, for a solution candidate(t, v(t), x(t)) at the elapsed time t. Whether or not the followingequation holds is determined for the found α.

$\begin{matrix}{0 \leq {v(t)} \leq {\frac{{V_{T_{\min}}(\alpha)} - {V_{T_{\min}}\left( {\alpha - 1} \right)}}{{X_{T_{\min}}(\alpha)} - {X_{T_{\min}}\left( {\alpha - 1} \right)}}{\quad{\left( {{x(t)} - {X_{T_{\min}}\left( {\alpha - 1} \right)}} \right) + {V_{T_{\min}}\left( {\alpha - 1} \right)}}}}} & \left\lbrack {{Number}\mspace{14mu} 1} \right\rbrack\end{matrix}$

This is obtained by approximating V_(Tmin)(x) with linear interpolation,using a result of the running time Tmin which gives an upper limit of avelocity by a position.

By the way, when a running curve is simply obtained by theabove-described method, since a running curve wherein the cumulativeenergy consumption amount is small is to be generated, a running curvewhich is highly operable to a driver is not always generated.

For example, in order to operate a vehicle according to the runningcurve to be generated, there is a possibility that the notch is to beoperated finely at each time, and accordingly, this method may beprobably not practical.

Therefore, in the present embodiment, the number of times of notchchangeover until that time is counted, as a selection condition for asolution candidate, and if one has the number not less than a definitevalue, the one is excluded from the solution candidate. For example,when the number of times of notch changeover for running between certainstations until a train arrives at a next station is set to not more than10 times, only a variable current_state[i] satisfying a condition that avariable storing the number of times of notch changeovercurrent_state[i].change_count≦10 is stored in the variable middle_state.

In addition, a notch continuous condition is a condition so as not tochangeover the notch at a short time interval, in the same manner as thenumber of times of notch changeover. When the notch continuous conditionis set to not less than 5 seconds, only the variable current_state[i]which satisfies a condition that a variable storing the notch continuoustime current_state[i].notch_contiuous_time≦5 is stored in the variablemiddle_state.

For this reason, in the above-described step S703, determination is madeto the whole solution candidates, using the position condition, thevelocity condition, the condition of the number of times of notchchangeover, the notch continuous time condition, and thereby only thosewhich satisfy these conditions are stored in the variable middle_state.

Further, in the step S704, the state (t, v(t), x(t)) at the elapsed timet+1, in the variable middle_state in which the solution candidatessatisfying the respective conditions are stored in the step S703, isquantized with respect to the velocity and the position, and thosehaving the quantized velocity and position, the number of times of notchchangeover, the notch continuous time which are the same are grouped,and only one having the smallest cumulative energy consumption amountout of those grouped has been left as a solution candidate.

In addition, in the present embodiment, such an extension as to selectthe notch so as not to exceed an upper limit value regarding aninstantaneous energy consumption amount can easily be made.

Here, a quantization processing will be described in more detail.

FIG. 15 is an explanation diagram of a quantization processing.

Since a position and a velocity are continuous values, in order toquantize them, the values thereof are quantized by a definite width,such as, 1 [m] regarding the position, and 0.1 [m/sec] regarding thevelocity, for example, and regarding the position, since the upper limitvalue Upper[t] and the lower limit value Lower[t] at the time t aredetermined, there is a method to quantize a position by dividing theposition between Upper[t] and Lower[t] by N. Here, the followingdescription will be made as a premise that each of a position and avelocity is quantized by a definite width.

In the present embodiment, since the four conditions of the positioncondition, the velocity condition, the condition of the number of timesof notch changeover, the notch continuous time condition are used, thestate of a solution candidate is defined by four axes, but since a statein not less than four dimensions is hard to be exemplified, here, thedescription will be made using the three conditions of the positioncondition, the velocity condition, the condition of the number of timesof notch changeover.

It is assumed that a result that solution candidates at a certainelapsed time t have been subjected to a pruning operation is in a stateas shown in FIG. 15(a).

The quantization processing divides a (v(t), x(t), n(t)) space into alattice state (rectangular state) as shown in FIG. 15(a), and the insideof the same region is assumed to be in the same state (condition). Here,n(t) is a number of times of notch changeover at the elapsed time t.

And, if a plurality of solution candidates exist in the same region, onehaving the smallest cumulative energy consumption amount in the sameregion is left as a solution candidate. As a result, it becomes possibleto prune more solution candidates, and thereby a processing time can bemore shortened.

In FIG. 15(b), a black dot indicates one which has remained as asolution candidate in each region.

In the step S705, whether the elapsed time t coincides with the runningtime T is determined, and if they are not coincident (step S705; No),the processing proceeds to a step S706, the elapsed time t isincremented, and the processing is transferred to the step S702 again.

In the step S705, if the elapsed time t coincides with the running timeT (step S705; Yes), one with the smallest cumulative energy consumptionamount is selected out of the solution candidates as an optimum solution(step S707).

And in the processing of the step S707, in order to finally select onehaving the small cumulative energy consumption amount, the solutioncandidates are sorted in ascending order (in order from a smaller one)regarding the cumulative energy consumption amount, and the one shouldbe selected from them based on the sorting result.

In addition, when a plurality of solution candidates exist at the endtime point, one wherein the cumulative energy consumptionamount+penalty(v, x) is the smallest is made an optimum solution.

Here, penalty(v(T), x(T)) indicates a penalty of an error between thestate (T, v(T), x(T)) at the elapsed time t and the terminal state (T,0, X). Generally, when a velocity and a position are calculated in anequation of motion, since a variable of a floating point type is used,the velocity and the position do not completely coincide with theterminal state in many cases. For the reason, the function penalty(v(T),x(T)) is prepared, and the cumulative energy consumption amountincluding errors is evaluated.

Regarding a method of determining penalty(v(T), x(T)), the followingequation is adopted in the same manner as Non-Patent Document 6

penalty(v(T),x(T)={v(T)}² +{x(T)−X} ²  [Number 2]

Next, a data format of the storage data of the running curve creationresult storage unit 16 will be described.

FIG. 16 is an explanation diagram of a format and a data example of thestorage data of the running curve creation result storage unit.

In the running curve creation result storage unit 16, data as shown inFIG. 16 is stored for each combination of the vehicle ID specifying avehicle (vehicle information), the ground ID specifying the groundinformation, and the running time T.

In more detail, in addition to the vehicle information, the groundinformation and the information of the running time, a shortest runningtime in the vehicle ID and the ground ID, and a velocity, a position, aninstantaneous power, a cumulative power, and a notch number at each timeinstant of the set running time are described. If the vehicle ID, theground ID and data of the running time T which have been inputted to therunning curve input processing unit 13 are in the state to be previouslystored in the running curve creation result storage unit 16, the data istransferred to the running curve creation result display unit 17,without creating a running curve, and the result should be displayed onthe running curve creation result display unit 17.

FIG. 17 is a diagram of a running curve which has been visualized, basedon the storage data of the running curve creation result storage unit.

And the display 28 functioning as the running curve creation resultdisplay unit 17 displays a result of a running curve of the running timeT which has been created in the energy saving running curve creationunit 15.

FIG. 18 shows an example of a running curve to be displayed on thedisplay.

A running curve in the railway business world is a curve wherein aposition is taken on the horizontal axis, and a velocity and a positionare plotted on the vertical axis.

Also in the present embodiment, a running curve is displayed as shown inFIG. 18.

In addition, in the display 28 functioning as the running curve creationresult display unit 17, the results of the cumulative energy consumptionamounts in the other running times can be compared, and the reductionrates in a cumulative energy consumption amount can be compared. In thepresent embodiment, focusing one between-station of a certain route forsimplification, a result of a running curve thereof has been displayed,but it is possible to easily create a running curve of the whole routefrom the respective results between stations.

In addition, when the inputted running time T is smaller than theshortest running time T_(min), since such running is not physicallyenabled, it is only necessary to display that such running is notenabled in the inputted running time on the running curve creationresult display unit 17.

In addition, when the inputted running time T is longer than theshortest running time Tmin, and when data of a running curve does notexist in the running curve creation result storage unit 16, it isnotified to the running curve input processing unit 13 that the datadoes not exist in the running curve creation result storage unit 16, andthereby the running curve input processing unit 13 may start the runningcurve creation processing.

As described above, according to the present embodiment, it becomespossible to create a running curve which is closer to an optimumsolution at high speed.

Further, it becomes possible to automatically create a running curvewhich is more operable to a driver.

In the above description, the running curve creation device 10 has beenrealized as a personal computer, but it can be realized as a server, orit can be configured to be realized as a so-called cloud on a network.

In the above-described configuration, it is not necessary to provide therunning curve creation result display unit in an integrated manner, butit is possible to configure to arrange such unit at a user side.

The control program to be executed in the running curve creation deviceof the present embodiment is presented while being recorded in acomputer readable recording medium, such as a CD-ROM, a flexible disk(FD), a CD-R, a DVD (Digital versatile Disk) in a file form of aninstallable format or an executable format.

In addition, the control program to be executed in the running curvecreation device of the present embodiment may be configured such thatthe control program is stored on a computer connected to a network suchas Internet, and is provided by being downloaded through the network. Inaddition, the control program to be executed in the running curvecreation device of the present embodiment may be configured such thatthe control program is provided or distributed through a network such asInternet.

In addition, the control program of the running curve creation device ofthe present embodiment may be configured such that the control programis provided while being incorporated in a ROM or the like.

The control program to be executed in the running curve creation deviceof the present embodiment has a module configuration including theabove-described respective units (the running curve input processingunit, the shortest time running curve creation unit, the energy savingrunning curve creation unit, the running curve creation result displayunit), and regarding an actual hardware, the CPU (processor) reads thecontrol program from the above-described storage medium and executes it,and thereby the above-described respective units are loaded on the mainstorage device, and the running curve input processing unit, theshortest time running curve creation unit, the energy saving runningcurve creation unit, the running curve creation result display unit areconfigured to be generated on the main storage device.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel embodiments described hereinmay be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the embodimentsdescribed herein may be made without departing from the spirit of theinventions. The accompanying claims and their equivalents are intendedto cover such forms or modifications as would fall within the scope andspirit of the inventions.

What is claimed is:
 1. In a running curve creation device to create arunning curve which can make a train having a prescribed vehiclecharacteristic run between a prescribed departure station and aprescribed arrival station in a prescribed running time in a smallercumulative energy consumption, the running curve creation devicecomprising: a shortest time running curve creation unit to create ashortest time running curve in which the train runs between the stationsin a shortest time, based on predetermined vehicle information andground information of the train; and an energy saving running curvecreation unit which selects, from the shortest time running curve and aplurality of solution candidates corresponding to states of the train ateach prescribed elapsed time since the train has departed from thedeparture station, a solution candidate having the relatively smallcumulative energy consumption in the prescribed running time, andcreates an energy saving running curve based on the selected solutioncandidate.
 2. The running curve creation device according to claim 1,wherein: the state of the train is a distance from the departure stationand a velocity of the train at the each prescribed elapsed time; and theenergy saving running curve creation unit creates the energy savingrunning curve by making, for each combination of a prescribed distancerange from the departure station and a prescribed velocity range, anyone state belonging to the each combination, as the solution candidaterepresenting the relevant combination.
 3. The running curve creationdevice according to claim 1, wherein: acceleration and deceleration ofthe train are performed by notch changeover; and the energy savingrunning curve creation unit excludes the state of the train in which anumber of times of notch changeover exceeds a prescribed number, fromthe solution candidate.
 4. The running curve creation device accordingto claim 1, wherein: acceleration and deceleration of the train areperformed by notch changeover; and the energy saving running curvecreation unit excludes the state of the train in which a continuous timeof the same notch is less than a prescribed continuous time, from thesolution candidate.
 5. The running curve creation device according toclaim 1, wherein: the vehicle information of the train includes a typeof the vehicle, a vehicle body weight, a riding rate, a number ofvehicles of a formation, a train length.
 6. The running curve creationdevice according to claim 1, wherein: the ground information includesinformation of a between-station distance, velocity limitationinformation including a section position and an upper limit velocitycorresponding to the relevant section position, and gradient informationin the advancing direction.
 7. The running curve creation deviceaccording to claim 1, wherein: the energy saving running curve creationunit obtains an upper limit value of a relation of the elapsed time anda position, from a result of the shortest time running curve created inthe shortest time running curve creation unit, obtains a lower limitvalue of the relation of the elapsed time and the position, from onewhich is obtained by moving the result of the shortest time runningcurve by the prescribed running time in the time direction, and selectsthe solution candidate having the relatively small cumulative energyconsumption from the upper limit value and the lower limit value.
 8. Ina running curve creation method to create a running curve which can makea train having a prescribed vehicle characteristic run between adeparture station and an arrival station in a prescribed running timewith a smaller cumulative energy consumption, the running curve creationmethod comprising: a shortest time running curve creation step to createa shortest time running curve in which the train runs between thedeparture station and the arrival station in a shortest time, based onvehicle information and ground information of the train; and an energysaving running curve creation step which selects, from the shortest timerunning curve and a plurality of solution candidates corresponding tostates of the train at each prescribed elapsed time since the train hasdeparted from the departure station, a solution candidate having therelatively small cumulative energy consumption in the prescribed runningtime, and creates an energy saving running curve based on the selectedsolution candidate.
 9. The running curve creation method according toclaim 8, further comprising: an acquisition step to acquire the groundinformation, the vehicle information and the prescribed running time;wherein: the shortest time running curve creation step has anacceleration limit curve creation step which, from information includingan initial condition of a velocity and a position in which a maximumacceleration is used, creates an acceleration limit curve indicating thevelocity and the position when the maximum acceleration is used; and adeceleration limit curve creation step which searches a condition tosatisfy a terminal condition, and creates a deceleration limit curveindicating the velocity and the position when a maximum deceleration isused.
 10. The running curve creation method according to claim 8,wherein: the energy saving running curve creation step, when the trainruns between the departure station and the arrival station in theprescribed running time, and when a position at an elapsed time t whenthe train runs between the stations in a shortest running time T_(min)is made Upper[t], and a relation which is obtained by moving (t,Upper[t]) in the shortest running time in parallel in the time axisdirection by a difference between the prescribed running time and theshortest running time T_(min) is made (t, Lower[t]), if an orbit of asolution in which the energy consumption amount in the prescribedrunning time becomes minimum is made (t, v(t), x(t)), satisfiesLower[t]≦x(t)≦Upper[t].
 11. The running curve creation method accordingto claim 8, wherein: the energy saving running curve creation stepfurther has a quantization step which quantizes a position and avelocity by dividing each of them by a definite width, and selects onehaving the smallest cumulative energy consumption amount in a dividedregion as one of the solution candidates.
 12. The running curve creationmethod according to claim 9, wherein: the condition of the solutionincludes a number of times of notch changeover, a notch continuationtime, in addition to the position and the velocity.
 13. The runningcurve creation method according to claim 8, wherein: acceleration anddeceleration of the train are performed by notch changeover; and theenergy saving running curve creation step excludes the state of thetrain in which a number of times of notch changeover exceeds aprescribed number, from the solution candidate.
 14. The running curvecreation method according to claim 8, wherein: acceleration anddeceleration of the train are performed by notch changeover; and theenergy saving running curve creation step excludes the state of thetrain in which a continuous time of the same notch is less than aprescribed continuous time, from the solution candidate.
 15. In acontrol program for controlling, by a computer, a running curve creationdevice to create a running curve which can make a train having aprescribed vehicle characteristic run between a prescribed departurestation and a prescribed arrival station in a prescribed running timewith a smaller cumulative energy consumption, the control program makingthe computer function as: shortest time running curve creation means tocreate a shortest time running curve in which the train runs between thestations in a shortest time, based on predetermined vehicle informationand ground information of the train; and energy saving running curvecreation means which selects, from the shortest time running curve and aplurality of solution candidates corresponding to states of the train ateach prescribed elapsed time since the train has departed from thedeparture station, a solution candidate having the relatively smallcumulative energy consumption in the prescribed running time, andcreates an energy saving running curve based on the selected solutioncandidate.